Question

1. In a Gallup poll, 1011 adults were randomly selected and asked if they consume alcoholic beverages. Of this sample, 64% said they did.
   1. Check requirements before computing confidence interval
   2. If requirements are met, use StatCrunch to obtain a 90% confidence interval for the proportion of all adults who consume alcoholic beverages.
   3. c. Write interpretation of the confidence interval.

Answer 1

We have the following summary

X: No. of adults who consumed alcoholic beverages

we directly have the sample proportion

= 64% n = 1011

Therefore the number of successes using the formula = x/ n

x = 647.04 = 647

(1) Since the 'n > 30' it is large

'np =x > 5'

we can use the normal approximation to calculate the confidence interval

(2) The steps to get the confidence interval on stat crunch are

1. Click on 'Stat' on the toolbar
2. Click on 'Proportions"
3. Then we choose 'one Sample' and then choose ''with summary' since we have summarized information of one sample and not a data
4. Then we see the calculator pop up. We input the no. of successes as the 'x' value and Observations as 'n'. Then click on 'next'
5. Since we want confidence interval we choose the second option.and we input '0.90' level. since it is 90%
6. Method 'Standard Wald' and then click 'next'

The summarized sheet with the calculation pops up

90% confidence interval results: p:proportion of successes for population Method:Standard -Wald
Proportion	Count	Total	Sample Prop.	Std. Err.	L.Limit	U.Limit
p	647	1011	0.64	0.015096	0.615169	0.664831

So the interval is

(3) We interpret that

we are 95% certain that the true proportion of adults consuming alcoholic beverages lies within the range (0.615,0.665).